A network for recursive extraction of canonical coordinates

Abstract

A network structure for canonical coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the canonical coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contributions of the already extracted coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional canonical coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set. q

A Multichannel Canonical Correlation Analysis Feature Extraction with Application to Buried Underwater Target Classification

“…In efforts to reduce the complexity of the problem, only the first half of the canonical correlations are used as features in the ensuing classification problem. This is justified since only the first few canonical correlations yield the greatest contribution to the linear dependence or mutual information between the data channels [6]. Figures 3(a) and (b) show the plots of canonical correlation features obtained for mine-like and non-mine-like objects via CCA and MCCA, respectively.…”

“…It is well-known that canonical correlation analysis (CCA) provides an elegant framework [6] for analyzing linear dependence and mutual information between two data channels. The results of [7] showed that MCCA provides a useful measure used to interpret and summarize the evolution of psoriasis in medical patients.…”

“…In the standard CCA [6], assuming that the previous (i − 1) th canonical coordinates are successfully extracted, the i th canonical coordinate is obtained by maximizing only one correlation, namely, a T i,1 R 12 a i,2 , while imposing the unit variance constraint, a…”

“…The optimal solution of (6) yields an eigenvalue problem which has no unique solution [5]. Certainly, using this constraint is analogous to the procedure adopted by [6] for two-channel CCA. However, the result is not a generalized eigensystem.…”

“…In the two-channel CCA case, this iterative procedure together with a deflation process [6] yields valid canonical coordinates. However, in the multichannel case a deflation process is still needed to generate these "canonical coordinates."…”